```Date: Mar 15, 2013 6:06 PM
Author: Virgil
Subject: Re: Matheology � 224

In article <37f8b921-a2db-46d0-a942-2d2ae5b727a3@k14g2000vbv.googlegroups.com>, William Hughes <wpihughes@gmail.com> wrote:> On Mar 14, 10:32 am, WM <mueck...@rz.fh-augsburg.de> wrote:> > <snip>> > >... consider the list of finite initial segments of natural numbers> >> > 1> > 1, 2> > 1, 2, 3> > ...> >> > According to set theory it contains all aleph_0 natural numbers in its> > lines. But is does not contain a line containing all natural numbers.> > Therefore it must be claimed that more than one line is required to> > contain all natural numbers. This means at least two line are> > necessary. There are no special lines necessary, but there must be at> > least two. In this case, however, we can prove, by the construction of> > the list, that every union of a pair of lines is contained in one of> > the lines. This contradicts the assertion that all natural numbers> > exist and are in lines of the list.> > > Nope.> > Nope, two lines are necessary but not sufficient.> > Two lines can never do a better job than 1.> > Any finite number of lines is necessary but not sufficient.> > Any finite number of lines can never do a better job than 1.> > An infinite number of lines is necessary and sufficient> > An infinite number of lines can do a better job than 1> > [In potential infinity things go> > Any number of findable lines is not sufficient> > An unfindable line is necessary and sufficient> > An unfindable line can do a better job than> any number of findable lines.  Or it would if you could find it.--
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